Physics constrained machine learning speeds optimized control with reliable rules
A Tutorial on Physics Constrained Machine Learning for Hybrid Modeling, Optimization, and Control
Machine LearningEmerging Technologies
Summary
Machine learning often ignores physical rules, leading to less reliable predictions. The authors created a new tool called KKT-HardNet that combines machine learning with strict physics rules to make predictions and control processes faster and more accurate. Their tool guarantees that the predictions obey physical laws by using special math steps that also make training the model efficient. They tested it on engineering problems and found it performed much better than previous methods.
What this means in practice
- •For process engineers: Use KKT-HardNet to create models that simulate, optimize, and control physical processes with guaranteed satisfaction of physical constraints and fast computation.
- •For control systems developers: Design real-time control algorithms that enforce safety and operational constraints exactly by integrating KKT-HardNet’s physics-based neural network projections.
Authors
Rahul Golder, Bimol Nath Roy, MM Faruque Hasan
Abstract
Physics-constrained machine learning (PCML) integrates domain knowledge, first-principles, and physical constraints into AI/ML models. In this work, we present a step-by-step tutorial of a modular PCML framework, KKT-HardNet, and illustrate how it could be used for hybrid modeling, process simulation, optimization and model predictive control in a single platform. KKT-HardNet combines fast inference capabilities of neural networks with guaranteed satisfaction of algebraic constraints through differential projection. It can handle heterogeneous data and enforce both linear and nonlinear equality and inequality constraints. The modular design supports custom neural-network backbones and user-defined projection mechanisms for PCML. To enable efficient end-to-end training, KKT-HardNet exploits implicit function theorem to backpropagate through the projection layer. This avoids computationally expensive automatic differentiation. This work also introduces an exact reduced-order Fischer-Burmeister reformulation and a primal-dual interior-point method as an alternative projection solve strategy. We also provide a diverse set of benchmarking problems for PCML in engineering applications. KKT-HardNet achieves orders of magnitude better performance in terms of both constraint satisfaction and inference time. The KKT-HardNet code and the benchmark datasets are available at https://github.com/souls-tamu/kkt-hardnet .